Full oscillation cycle phase noise analysis of differential CMOS LC oscillators

This paper analyzes the phase noise of the widely used differential LC oscillator topology and presents brief equations describing phase noise over the entire oscillation period. The findings show that if a capacitance is present at the source node of the differential pair, two phenomena occur that increase the phase noise: the switch time increases, lengthening the interval spent in a noisy balanced state and increasing the transistor noise excess factor; and at higher frequencies the unbalanced state starts to contribute phase noise. The analysis is based upon the superposition of piecewise linear equations using the EKV transistor model, which includes a concise formulation of the noise excess factor.